# Gauge Freedom within the Class of Linear Feedback Particle Filters

arXiv: https://arxiv.org/abs/1903.06689 · HTML: https://mlsanity.com/paper/1903.06689/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Mar 2019.

## Built on by (most cited first, 1 of 1)

- [On gauge freedom, conservativity and intrinsic dimensionality estimation in diffusion models](https://mlsanity.com/paper/2402.03845/) (2024)

## Abstract (arXiv)

Feedback particle filters (FPFs) are Monte-Carlo approximations of the solution of the filtering problem in continuous time. The samples or particles evolve according to a feedback control law in order to track the posterior distribution. However, it is known that by itself, the requirement to track the posterior does not lead to a unique algorithm. Given a particle filter, another one can be constructed by applying a time-dependent transformation of the particles that keeps the posterior distribution invariant. Here, we characterize this gauge freedom within the class of FPFs for the linear-Gaussian filtering problem, and thereby extend previously known parametrized families of linear FPFs.